Optimal harvesting policy for the Beverton--Holt model

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Population dynamics are crucial for sustainable resource management.
• Periodic coefficients in population models reflect environmental variability.
• The Beverton-Holt model is a standard for fisheries and population studies.

Purpose of the Study:

• To analyze population exploitation using the Beverton-Holt difference equation with periodic coefficients.
• To investigate optimal harvesting policies for discrete population models.
• To compare harvesting strategies between discrete (Beverton-Holt) and continuous (logistic) models.

Main Methods:

• Modeling population dynamics with the Beverton-Holt difference equation and periodic coefficients.
• Analyzing the existence and global stability of positive periodic solutions.
• Developing a novel approach to optimize annual sustainable yield.
• Deriving and optimizing the sustainable yield for the harvested Beverton-Holt model.

Main Results:

• The harvested logistic equation with periodic coefficients exhibits a unique, globally attracting positive periodic solution.
• The harvested Beverton-Holt model also yields a unique, globally attracting positive periodic solution.
• Optimization of sustainable yield for the Beverton-Holt model yields different results compared to continuous logistic models.

Conclusions:

• Periodic coefficients in population models necessitate specific analytical approaches.
• Optimal harvesting strategies for discrete population models like Beverton-Holt differ from continuous models.
• This research provides a foundation for distinct management strategies in discrete population dynamics.